A193039
G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n*A(-x)^A002024(n+1), where A002024 is defined as "n appears n times.".
Original entry on oeis.org
1, 1, 1, 2, 5, 13, 34, 91, 251, 709, 2035, 5913, 17366, 51483, 153858, 463001, 1401751, 4266619, 13048709, 40078032, 123570957, 382331356, 1186699353, 3694028136, 11529606672, 36073811897, 113123222246, 355485228001, 1119275386080, 3530531671842
Offset: 0
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 34*x^6 + 91*x^7 +...
The g.f. satisfies:
1 = A(-x) + x*A(-x)^2 + x^2*A(-x)^2 + x^3*A(-x)^3 + x^4*A(-x)^3 + x^5*A(-x)^3 + x^6*A(-x)^4 +...+ x^n*A(-x)^A002024(n+1) +...
where A002024 begins: [1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,...].
The g.f. also satisfies:
1-x = (1-x)*A(-x) + x*(1-x^2)*A(-x)^2 + x^3*(1-x^3)*A(-x)^3 + x^6*(1-x^4)*A(-x)^4 + x^10*(1-x^5)*A(-x)^5 +...
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{a(n)=local(A=[1]);for(i=1,n,A=concat(A,0);A[#A]=polcoeff(sum(m=1,#A,(-x)^m*Ser(A)^floor(sqrt(2*m)+1/2) ),#A));if(n<0,0,A[n+1])}
A193040
G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n*A(-x)^A131507(n), where A131507 is defined as "2*n+1 appears n times.".
Original entry on oeis.org
1, 1, 2, 7, 29, 129, 600, 2889, 14293, 72228, 371208, 1934236, 10194853, 54258010, 291175463, 1573878211, 8560931357, 46825444031, 257386132988, 1421034475176, 7876770462043, 43817869686744, 244552276036950, 1368945007588648, 7683977372121530
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 29*x^4 + 129*x^5 + 600*x^6 +...
The g.f. satisfies:
1 = A(-x) + x*A(-x)^3 + x^2*A(-x)^3 + x^3*A(-x)^5 + x^4*A(-x)^5 + x^5*A(-x)^5 + x^6*A(-x)^7 +...+ x^n*A(-x)^A131507(n) +...
where A131507 begins: [1,3,3,5,5,5,7,7,7,7,9,9,9,9,9,11,...].
The g.f. also satisfies:
1-x = (1-x)*A(-x) + x*(1-x^2)*A(-x)^3 + x^3*(1-x^3)*A(-x)^5 + x^6*(1-x^4)*A(-x)^7 + x^10*(1-x^5)*A(-x)^9 +...
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{a(n)=local(A=[1]);for(i=1,n,A=concat(A,0);A[#A]=polcoeff(sum(m=1,#A,(-x)^m*Ser(A)^(2*floor(sqrt(2*m)+1/2)-1) ),#A));if(n<0,0,A[n+1])}
A193050
G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n*A(-x)^A003059(n+1), where A003059 is defined by "n appears 2n-1 times.".
Original entry on oeis.org
1, 1, 1, 2, 4, 8, 17, 38, 87, 204, 489, 1191, 2938, 7328, 18448, 46809, 119583, 307324, 793965, 2060770, 5371156, 14051901, 36887289, 97131351, 256488187, 679046184, 1802047427, 4792800096, 12773166908, 34106055493, 91228795961, 244427136822, 655900969465
Offset: 0
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 38*x^7 +...
The g.f. satisfies:
1 = A(-x) + x*A(-x)^2 + x^2*A(-x)^2 + x^3*A(-x)^2 + x^4*A(-x)^3 + x^5*A(-x)^3 + x^6*A(-x)^3 + x^7*A(-x)^3 + x^8*A(-x)^3 + x^9*A(-x)^4 +...+ x^n*A(-x)^A003059(n+1) +...
where A003059 begins: [1, 2,2,2, 3,3,3,3,3, 4,4,4,4,4,4,4, 5,...].
The g.f. also satisfies:
1-x = (1-x)*A(-x) + x*(1-x^3)*A(-x)^2 + x^4*(1-x^5)*A(-x)^3 + x^9*(1-x^7)*A(-x)^4 + x^16*(1-x^9)*A(-x)^5 +...
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{a(n)=local(A=[1]); for(i=1, n, A=concat(A, 0); A[#A]=polcoeff(sum(m=1, #A, (-x)^m*Ser(A)^(1+sqrtint(m-1)) ), #A)); if(n<0, 0, A[n+1])}
Showing 1-3 of 3 results.
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